42.10 ImagesRepresentative

ImagesRepresentative( map, elm )

ImagesRepresentative returns a representative of the set of images of elm under map, i.e., a single element img, such that img in Images( map, elm ) (see Images). map may be a multi valued mapping.

    gap> g := Group( (1,2,3,4), (2,4), (5,6,7) );;  g.name := "g";;
    gap> p4 := MappingByFunction( g, g, x -> x^4 );
    MappingByFunction( g, g, function ( x )
        return x ^ 4;
    end )
    gap> i4 := InverseMapping( p4 );
    InverseMapping( MappingByFunction( g, g, function ( x )
        return x ^ 4;
    end ) )
    gap> IsMapping( i4 );
    false    # 'i4' is multi valued
    gap> ImagesRepresentative( i4, () );
    () 

ImagesRepresentative calls
map.operations.ImagesRepresentative( map, elm ) and returns this value.

The default function called this way is MappingOps.ImagesRepresentative, which calls Images( map, elm ) and returns the first element in this set. Look in the index under ImagesRepresentative to see for which mappings this function is overlaid.

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